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A promising avenue to measure the total, and potentially individual, mass of neutrinos consists of leveraging cosmological datasets, such as the cosmic microwave background and surveys of the large-scale structure of the universe. In order to obtain unbiased estimates of the neutrino mass, however, many effects ought to be included. Here we forecast, via a Markov Chain Monte Carlo likelihood analysis, whether measurements by two galaxy surveys: DESI and {\it Euclid}, when added to the CMB-S4 experiment, are sensitive to two effects that can alter neutrino-mass measurements. The first is the slight difference in the suppression of matter fluctuations that each neutrino-mass hierarchy generates, at fixed total mass. The second is the growth-induced scale-dependent bias (GISDB) of haloes produced by massive neutrinos. We find that near-future surveys can distinguish hierarchies with the same total mass only at the 1𝜎 level; thus, while these are poised to deliver a measurement of the sum of neutrino masses, they cannot significantly discern the mass of each individual neutrino in the foreseeable future. We further find that neglecting the GISDB induces up to a 1𝜎 overestimation of the total neutrino mass, and we show how to absorb this effect via a redshift-dependent parametrization of the scale-independent bias.